The generator matrix
1 0 1 1 1 2 1 1 0 0 1 1 1 0 1 2 1 1 1 1 0 1 0 1 1 X 1 X 1 X 1 X 1 1 0 1 1 1 1 1 X+2 X 1 X+2 1 X+2 X 1 1 1 1 0 2 1 X 1 0 1 2 1 X 1 1 X+2 1 1 X 2 1 0 1 1 1 1 1 1 2 0 X+2 X 1 2 1 0 1 X X 1 2 1
0 1 1 0 1 1 2 X+1 1 1 0 X+3 3 1 0 1 2 1 1 0 1 3 1 X X+1 1 X 1 X+3 1 X 1 X+1 0 1 X+1 X+2 X+1 X+1 X+2 1 1 X+1 1 1 1 1 X+2 1 X+1 0 1 1 X+2 1 2 1 0 1 X 1 2 X+2 1 X 0 1 1 X+1 1 3 0 X X X+3 X 1 1 1 1 1 1 X X X+3 1 1 X 0 0
0 0 X 0 0 0 0 2 2 2 0 0 2 X X+2 X+2 X X X+2 X+2 X+2 X+2 X+2 X+2 X+2 2 0 X+2 X+2 0 2 0 0 X+2 2 0 X+2 X+2 2 2 X X+2 X+2 0 0 2 0 0 2 2 X X+2 X 0 X 2 X+2 X 0 X+2 2 X X X 2 2 0 X 2 X+2 0 X X+2 2 X 2 X+2 0 2 X+2 0 2 X+2 0 X X+2 X X X 0
0 0 0 X 0 0 2 2 X X X+2 X+2 X+2 X+2 2 X+2 X+2 X 0 X 2 X+2 0 0 X+2 0 0 2 X 2 0 X+2 2 X+2 X 0 2 X X 0 2 X+2 0 X 2 X+2 0 X X 2 X+2 2 0 X X+2 0 X X+2 X X+2 X+2 0 X+2 X X+2 0 X 2 X X+2 X+2 2 0 2 2 X 0 0 2 X 0 X+2 X X X X+2 X+2 2 X+2 0
0 0 0 0 X X+2 X+2 2 X+2 0 X+2 0 X 2 X+2 X+2 X X+2 X 2 X 0 2 2 2 X+2 X+2 X+2 X 2 2 0 X X X 2 X 0 X X 2 0 0 X 0 0 X+2 X+2 0 X+2 2 0 X X X X 0 X+2 0 X+2 2 2 X+2 X 0 2 X+2 0 0 0 X 2 X+2 2 2 0 X+2 2 X 2 0 2 X+2 2 X X 2 0 0 0
generates a code of length 90 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 82.
Homogenous weight enumerator: w(x)=1x^0+100x^82+108x^83+257x^84+240x^85+397x^86+232x^87+370x^88+244x^89+413x^90+206x^91+332x^92+206x^93+335x^94+174x^95+207x^96+58x^97+82x^98+28x^99+28x^100+12x^101+10x^102+14x^103+18x^104+6x^105+4x^106+6x^107+2x^108+2x^109+2x^110+1x^116+1x^130
The gray image is a code over GF(2) with n=360, k=12 and d=164.
This code was found by Heurico 1.16 in 1.6 seconds.